Computational Mechanics of Traumatic Brain
Injury under Impact Loads
Hesam S. Moghaddam*
Northern Arizona University, Mechanical Engineering Department, Flagstaff, AZ, USA
Email: [email protected]
Asghar Rezaei Mayo Clinic, Department of Physiology and Biomedical Engineering, Rochester, MN, 55905
Email: [email protected]
North Dakota State University, Mechanical Engineering Department, Fargo, ND, USA
Email: [email protected], [email protected]
Abstract—A finite element (FE) study was performed to
investigate the dynamic response of the brain under impact
loading using computational mechanics to better
understand the mechanisms of impact induced traumatic
brain injury (iTBI). North Dakota State University Finite
Element Head Model (NDSUFEHM) was used to
investigate the pressure and stress responses of the brain
under different impact conditions. The impacts were
carried out at a 45º-tilted orientation using two different
impact velocity, 10 m/s and 13 m/s, which resulted in a total
of two different impact scenarios. LS-Dyna nonlinear FE
solver and LS-PrePost were employed to perform all
simulations, record data and visualize results. Specifically,
the intracranial pressure (ICP), maximum shear stress
(MSS), were recorded and analyzed for two different
impact velocities. These biomechanical responses were
recorded at different locations on and inside the brain to
starting from the impact site (coup) to the opposite site
(countercoup). This was done to analyze the variations of
ICP and MSS through the brain in order to understand the
role of these parameters in injury mechanisms. The impact
severity was shown to have more effect on the level of
pressure response while its effect on peak MSS was not
much. ICP variation was linear between coup and
countercoup sites. It was observed that unlike pressure,
shear stress traveled slower through the brain tissue. Our
findings suggested that using only one biomechanical
parameter can’t justify the fidelity of the FE head models.
Index Terms—computational mechanics, traumatic brain
injury, shear stress, intracranial pressure, finite element
analysis
I. INTRODUCTION
Impact induced TBI (iTBI) which accounts for 75%
of the TBI cases, is a localized injury which results in
from contact of the brain with the skull due to the
relative motion of the brain with respect to skull upon
acceleration/deceleration of the head upon impact.
Manuscript received May 1, 2018; revised July 4, 2019.
This type of brain injury, is visible and can be
detected by routine imaging techniques such as
Magnetic resonance imaging (MRI) or Computed
Tomography (CT) scans. The iTBI can appear in the
form of skull fracture, rupture of blood vessels inside
and on the brain surface (intracerebral and subdural
hematoma), and cerebral contusion [1]. The severity
of iTBI varies by several parameters such as the
anatomy of the heads, the intensity of the force
applied on the head, and the location of impact [2]. The
iTBI mainly involves two stages of brain injury: primary
and secondary brain injuries. Primary injury refers to the
damage of the brain tissue and blood vessels at the
instant of the assault due to the structural displacement of
the brain [3]. On the other hand, the second injury which
is perceived as the indirect mechanism injury, involves
the deterioration of the cellular activities such as blood-
brain barriers damage and dysfunction of neurons. The
common causes of iTBI are the car accidents, falls, and
sport-related accidents such as football and hockey.
Several in vivo animal studies, in vitro experiments,
human cadaver and volunteer tests have been performed
on the impact induced TBI [4,5]. As kinematic-based
metrics rely on the linear and angular accelerations of the
head, they neglect the material properties and behavior of
different head components, especially the brain. Due to
structural inhomogeneity of the human head and the
intrinsic differences of head components in terms of
shape, material, and tolerance, different parameters such
as the impact velocity (intensity), location
(directionality), the type of blunt impact (struck against
or struck by) can affect the mechanical response of the
head [6,7]. Accordingly, these variations would influence
the stress and strain wave propagation, as well as the
intracranial pressure (ICP) gradient distribution
throughout the brain tissue, which would produce
different levels of injury. As a common criterion in the
literature, the head acceleration is utilized for defining
International Journal of Mechanical Engineering and Robotics Research Vol. 8, No. 6, November 2019International Journal of Mechanical Engineering and Robotics Research Vol. 8, No. 6, November 2019
921© 2019 Int. J. Mech. Eng. Rob. Resdoi: 10.18178/ijmerr.8.6.921-928
Mariusz Ziejewski, and Ghodrat Karami
various injury thresholds [8]. It is postulated, however,
that the head trauma, such as diffuse brain injury,
subdural hematoma, and contusion, is mainly associated
with brain tissue parameters such as shear stress rather
than head kinematics [9,10]. Impact loads which
propagate inside the cranium and pass through different
layers of head components also create stress waves. It is
stated that the dynamically induced pressures at the coup
and countercoup sites may generate stresses high enough
to cause injuries in the brain [11]. Fig. 1 shows potential
injury mechanisms for impact-induced TBI in a
schematic manner. The dynamic loads in the form of
dilatational and distortional stress waves have also been
proposed as main contributors to TBIs [12,13]. However,
due to moral and technical complexities in evaluation of
tissue response of human head, the kinematical
parameters of the head motion under assault are
commonly used as the injury predictors. Nahum and Smith [14] performed cadaveric impact
tests on 10 different seated cases. They used several
impactors with masses ranging between 5.18 to 23.09 kg
and constant impact velocities varying from 3.56 to 12.5
m/s. The head was inclined 45 degrees about its
horizontal plane and a frontal impact was carried out on
the frontal bone and brain ICP was recorded. The peak
force delivered to the head was reported to be between
2.9 to 12 kN with a duration of 3-18 ms. They reported
the peak positive pressure at the coup site and the peak
negative pressure at the counter-coup site and reported a
linear relationship between the linear head acceleration
and the ICP. Stalnaker et al. [15] carried out cadaveric
tests on 15 seated cadavers using a 10 kg impactor. The
peak force was recorded as 4.2 and 14.6 kN with the
durations of 3.2 and 10.6 ms. They reported a linear
acceleration of 140 and 532 G’s and reported the peak
ICP as 140 kPa.
Figure 1. Mechanisms of impact-induced TBI and possible injuries
Despite such valuable studies, the cause of TBIs is too
complex to be experimentally explained. Accordingly,
mathematical modeling and computational algorithms
have found a great attraction in the past few decades.
One of the most effective and advanced computational
mechanic methods for studying the mechanical response
of the human brain to dynamic loads such as impact and
blast, is the finite element analysis (FEA) [16-18]. FEA
codes have been extensively used not only to evaluate
the kinematics of the head, but also to assess the
deformation of the soft tissue of the brain and different
head components to provide estimates of the stresses and
strains inside the brain.
Zhang et al. [5] reconstructed actual American
football field incidents and used their kinematical data,
as the input for their complex FE head model, to evaluate
the mechanical response of the head. They recorded the
shear stress and pressure response of the brain to several
impacts and proposed some injury predictors and mTBI
thresholds based on both kinematical and tissue-level
parameters of the head. High shear stress levels were
observed at the brainstem and thalamus locations. The
linear head acceleration was found to have a greater
effect on the ICP response of the brain. Finally, a
threshold value of 7.8 kPa for the shear stress was
asserted as the tolerance level for 50% probability of
mTBI. El Sayed et al. [19] used a 3D FEHM, to carry
out impact simulations for frontal and oblique impacts to
evaluate the brain tissue response. The skull and the CSF
were modeled by a hyperviscoelastic constitutive model.
They reported that with respect to the frontal impact, the
brain tissue predicted higher pressure responses at both
coup and countercoup sites for the oblique impact, which
was indicative of focal and diffuse damages in these sites.
Sarvghad-Moghaddam et al. [2] investigated the effect of
directionality on the response of the brain to impact loads.
They used a 3D FE head model with neck attached.
Using identical impact velocity of 2.2 m/s, they impacted
the head model from front, back and side and reported
that while the predicted tissue responses in the front and
side impacts were quite close, the brain response to the
back impact was significantly lower than those predicted
in other scenarios, especially in terms of the shear stress.
Their results confirmed directional dependence of the
head response as they observed that for the back impact,
the head was less prone to severe injuries, while front
and side impacts predicted severe injury conditions.
The main focus of current study is to investigate the
mechanisms of impact-induced traumatic brain injury
using computational mechanics in terms of the
biomechanical responses, ICPs and shear stresses, of the
FE head to impact. Variations of ICPs and shear stresses
in different parts of the brain were monitored and
recorded while the head model was impacted with two
different impact velocities.
II. COMPUTATIONAL METHODOLOGY AND MATRIALS
A. FE Head Model
The human head model used for this research was
originally developed by Horgan and Gilchrist [20] from
the Computed Tomography (CT) data provided by
Visible Human Project, by 0.3 mm increment in the
coronal plane. After stacking up the CT data,
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thresholding and interpolation techniques were
performed to identify the voxels representation of the
tissue. Smooth triangle surfaces of the head were then
created by interpolation through the voxels. The CT data
was employed to make a polygonal model of the head
using VTK software. After smoothing the polygonal
model, it was converted into IGES format and was
imported in the MSC/Patran for meshing. The North
Dakota State University Finite Element Head Model
(NDSUFEHM), was developed in 2010 by adding the
neck bone and skin, facial skin. The head model was
discretized using HyperMesh using a total of 38,379
shell and brick elements. The anatomical components, as
well as the discretization properties of all the head/neck
components are presented in Table I. NDSUFEHM
includes the major anatomical features of the human
head and neck such as scalp, skull, dura mater, falx,
tentorium, pia mater, CSF, brain, neck- bone, neck
muscle, facial bone, and facial skin (Fig. 2).
Figure 2. FE discretization of human head components for
NDSUFEHM.
One of the challenges in developing exact FE models
of the human head is the accurate modeling of the
interfaces among different head components. To this end,
it is very important that the CSF layer is properly
modeled. As mentioned before, CSF is a water-like fluid
layer which surrounds the cranial space and separates the
skull from the brain. It acts as a natural shock absorber
which provides the relative displacement of the brain
with respect to the skull [21]. In our research, CSF was
modeled using 8-noded brick elements with fluid-like
properties, which allows for the relative skull/brain
motion, agrees with impact experiments [22]. To comply
with the anatomical characteristics of the head, while tied
surface-to-surface contact algorithm was employed to
replicate the interfaces between the scalp and skull, the
skull and dura, and the brain and pia, tied node-to-
surface was employed for defining the contacts among
the dura-falx-tentorium components, which provides an
application of both compressive and tensile loads on the
brain [1].
B. Material Models
Developing an accurate constitutive model for the
brain tissue has always been a challenge and numerous
studies have been performed to improve the modeling of
head components in order to better predict the human
head behavior under different loading conditions [23,24].
In the current study, linear elastic constitutive
properties used for NDSUFEHM components such as the
scalp, skull, pia and dura mater, tentorium, CSF, as well
as the neck bone and muscle are adopted from the works
of Zhang et al. [5] and Horgan and Gilchrist [20]. The
mechanical properties of these components are described
in Table II. However, a hyper-viscoelastic material
model is utilized to better capture the nonlinear behavior
of the brain tissue. This model, as also employed by
Chafi et al. and Moghaddam et al. [1,22], develops
effective constitutive properties in terms of the large
deformations due to the dynamic blast loading.
Intracranial pressure, defined as the pressure imposed by
CSF, and blood on the brain is one of the major
parameters in evaluation of the TBI as elevated ICP can
induce severe neurological damages.
TABLE I. FINITE ELEMENT CHARACTERISTICS AND EMPLOYED
MATERIAL MODELS FOR HEAD COMPONENTS
Tissue Constitutive
model FE model
# of
Elements
Scalp Linear elastic 6 mm
Solid element 5938
Skull Linear elastic Solid element 8305
Dura, falx,
tentorium Linear elastic
1 mm thick
shell element 2590
Pia Linear elastic 1 mm thick
shell element 2754
CSF Linear elastic &
Viscoelastic
1.3 mm thick
solid element 3354
Spinal cord Linear Elastic Solid elements 496
Brain Hyperviscoelast
ic Solid element 7302
Neck bone Linear elastic 6 mm thick
solid element 496
Neck Muscle
Linear elastic Solid element 3772
Facial Bone Linear elastic 2mm
Solid element 1124
Facial Skin Linear elastic Solid element 2248
Intracranial pressure is defined as the hydrostatic
pressure imposed on the brain mainly due to the fluid-
like behavior of the tissue. The hydrostatic pressure, P, is
the mean stress of three principal stresses 𝜎1, 𝜎2 𝑎𝑛𝑑 𝜎3
[24]:
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𝑃 = −𝜎1+𝜎2+𝜎3
3 (1)
TABLE II. MECHANICAL PROPERTIES OF HEAD COMPONENTS
Head
Component
Density
(g/cm3)
Elastic
Modulus
(GPa)
Poisson’s Ratio
Scalp/ Skin 1.2 0.0167 0.42
Skull 1.21 8.0 0.22
Dura, falx,
tentorium 1.133 0.0315 0.45
Pia mater 1.133 0.0115 0.45
Facial bone 2.10 5.54 0.22
Cervical Vertebrae
2.5 0.354 0.3
CSF 1.004 2.19
Bulk Modulus 0.499
In current material modeling, the Mooney–Rivlin
formulation is adopted for describing the hyperelastic
nonlinear behavior of the brain tissue while the Maxwell
constitutive law is applied towards modeling the linear
viscoelastic behavior of biological tissues. Accordingly,
the resulting Cauchy stresses from both approaches are
employed to describe the brain response under applied
loadings. The material model used in this study
correlated perfectly to the intrinsic behavior of the brain
regarding its mostly incompressible behavior and
sustainability under large deformations. The parameters
for the Mooney-Rivlin constitutive equation are
determined from the work of Mendis et al. [23].
The strain energy density function governing the
Mooney-Rivlin constitutive approach for the
incompressible, homogenous and isotropic materials is
described by:
𝑊 = 𝐶10(𝐼1̅ − 3) + 𝐶01(𝐼2̅ − 3) +𝐾
2(𝐽3 − 1)2 (2)
where 𝐶10 and 𝐶01 and K represent the material constants
evaluated experimentally, 𝐼1̅ and 𝐼2̅ are the first and
second invariants of the Cauchy tensor and 𝐽3 is the
elastic volume ratio. The Cauchy stress corresponding to
the nonlinear hyperelastic model is obtained as:
𝜎 = −𝜕𝑊
𝜕𝜀 (3)
where W is the strain energy potential of Mooney-Rivlin
and 𝜀 represents the Green’s strain tensor. The
parameters for the Mooney-Rivlin constitutive equation
is determined from the work of Mendis et al. [23] and are
shown for the brain tissue in Table III. On the other hand,
applying the Maxwell model for the linear viscoelastic
behavior of the tissue, one can find the resulting Cauchy
stress tensor:
𝜎𝑖𝑗 = 𝐽𝐹𝑖𝑘𝑇 ∙ 𝑆𝑘𝑚 ∙ 𝐹𝑚𝑗 (4)
where J depicts the transformation Jacobian, F indicates
the gradient tensor of deformation and S is the second
Piola–Kirchhoff stress tensor. The rate effects captured
by this constitutive model are formulated using a
convolution integral in terms of the second Piola–
Kirchhoff stress tensor, 𝑆𝑖𝑗 and the Green’s strain tensor,
𝐸𝑘𝑙 as follows:
𝑆𝑖𝑗 = ∫ 𝐺𝑖𝑗𝑘𝑙(𝑡 − 𝜏)𝜕𝐸𝑘𝑙
𝜕𝜏
𝑡
0𝑑𝜏 (5)
with 𝐺𝑖𝑗𝑘𝑙(𝑡 − 𝜏) indicating the relaxation functions at
various stress levels.
The Prony series can be used to describe the relaxation
functions which are employed to evaluate the Cauchy
stress tensor:
𝐺(𝑡) = 𝐺0 + ∑ 𝐺𝑖𝑒−𝛽𝑖𝑡𝑛
𝑖=1 (6)
where G is the shear modulus and 𝛽 is the decay
parameter [14]. The data has been widely used in related
literature and has shown to provide reasonable results
[22, 25]. In order to prevent the rigid body motion and
keep the stability of the solution, the inferior surface of
the neck is constrained in all directions (Fig. 3).
TABLE III - MECHANICAL PROPERTIES OF HYPER-VISCOELASTIC
BRAIN MATERIAL
𝐶10
(Pa)
𝐶01
(Pa)
𝐺1
(kPa)
𝐺2
(kPa)
𝛽1
(s−1)
𝛽2
(s−1)
K
(GPa)
3102.5 3447.2 40.744 23.385 125 6.6667 2.19
C. Impact Modeling
All the impact simulations were carried out using a
rigid cylindrical impactor with a mass of 5.6 kg. Studies
have shown that besides the severity of impact which
clearly affects the brain response, the direction of impact
would also change the brain tissue response [2,5]. The
impacts were carried out at a 45º-tilted orientation using
two different impact velocity, 10 m/s and 13 m/s, which
resulted in a total of two different impact scenarios.
NDSUFEHM was impacted at 45º from Frankfort
plane to generate a contact force similar to the one in the
study of Nahum et al. [14] with the maximum force of
around 8 kN on the skull, and the brain responses under
the applied force were monitored. Ward et al. [26]
proposed an injury criterion based on the ICP threshold
of 173 to 235 kPa (i.e., moderate to severe injury
corresponding to AIS 3–4 and AIS 5–6, respectively) for
TBI. According to this criteria, the predicted tissue
responses for the loading employed in this study
approached the moderate TBI threshold. The second
impact scenario was simulated by impacting the head
model in the same orientation but at a higher velocity of
13 m/s. The aim was to create contact force of around
10.1 kN on the skull in these two impacts in order to
create injury levels of severe TBI, or fatality. The
waveforms of the brain tissue responses in terms of ICP
and shear stress were recorded at different locations on
and inside the brain and compared. In addition, the peak
pressure and shear stress values were monitored at seven
equally spaced locations in the brain across a line on the
sagittal plane, connecting the coup and the countercoup
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sites (Fig. 3). The results could help gain a better
understanding of the mechanism that happens inside the
brain as a result of blunt impacts.
Figure 3. (a) Boundary conditions and head orientation at 45º from
Frankfurt plane; (b) sagittal plane of the brain and the schematic view
of the locations that the biomechanical parameters are extracted.
III. RESULTS AND DISCUSSION
A. ICP Response of the Brain
Figure 4. (a) ICP variations at different locations inside the brain on
the connecting line of coup-countercoup sites when the impact velocity
is 10 m/s; (b) Maximum pressure at different locations of the brain
from coup (point 1) to countercoup site (point 7); (c) ICP variations at different locations for 13 m/s impact velocity
The coup-countercoup ICPs were recorded for both
simulations. As illustrated in Fig. 4(a), the responses of
the brain were monitored at 7 equally distant locations on
the coup-countercoup connecting line, with the first point
at the site of impact (coup), and the 7th point located at
the opposite site of the impact (countercoup). The
highest positive and negative pressure values were
observed at the coup and countercoup regions,
respectively, and started to decrease towards the mid-
brain region. The peak ICP values, recorded at different
locations of the brain across the so-called connecting line,
are compared in Fig. 4(b). The pressure response showed
a linear variation inside the brain from the site of impact
(point 1) to the opposite site of impact (point 7) and
approached zero somewhere in the middle of the brain
(between point 4 and 5), which was indicative of the
interaction of positive and negative pressures. The
maximum inflicted pressures always happen on the outer
surface of the brain at these two sites and as far as the
ICP thresholds are concerned, the amount of pressures
inside the brain is, therefore, of no interest.
In the second impact scenario, the simulation was
replicated in the same orientation, but the velocity of the
impactor was increased by 30% to about 13 m/s. Fig. 4(c)
illustrates the variation of pressure at the same locations
across the coup-countercoup connecting line for the
high-velocity impact at 45º from Frankfort plane.
B. Shear Stresss Response of the Brain
Fig. 5(a) shows shear stress variations inside the brain
at the aforementioned locations. A phase lag was
observed in the generation of maximum shear stress
waves, due to the low shear modulus of the brain tissue,
with respect to the ICP pattern. To better understand the
effect of impact severity on the tissue response of the
brain, the impact velocity was increased to 13 m/s in the
previous scenario, while other conditions were kept the
same. Fig. 5(b) represents the shear response for the
high-velocity impact.
The shear response followed a pattern similar to those for
the low-velocity impact in Fig. 5(a). The maximum shear
stresses were 1.6 and 2.5 kPa in the low and high
velocity impacts, respectively.
Fig. 6 illustrates the distribution of ICP and shear
stress in different regions of the brain. This Fig. clearly
shows the band like layout of the pressure distribution all
over the brain such that different regions are made.
However, for shear stress, the distribution is not uniform
and the maximum occurred at the brainstem.
The contact force on the head induced by a blunt
impact leads to the sudden head motion and, as a result,
the relative normal displacement of the brain with
respect to the skull [7]. It was previously suggested that
the relative brain/skull motion could contribute to the
development of ICP variations inside the brain [7, 27].
Our ICP results showed that the variation pattern of
pressure from coup to countercoup site is linear. The
increase in the velocity of the impactor by 30% to about
13 m/s, at which serious injury or death occurs [26],
contributed to similar results by the head models,
emphasizing the independency of ICP variation pattern
(a) (b)
-150
-100
-50
0
50
100
150
200
0 2 4 6 8ICP
(k
Pa)
Time (ms)
-150
-100
-50
0
50
100
150
200
1 2 3 4 5 6 7ICP
(kP
a)
Points of Interest
-300
-200
-100
0
100
200
300
400
0 2 4 6 8ICP
(kP
a)
Time (ms)
(b)
(a)
(c)
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on the severity of the impact load. Figs. 4(a) and 4(c)
illustrate how fast the pressures created at both coup and
countercoup sites can travel throughout the brain. The
rise in the respective positive and negative pressures at
points 1 and 7 was observed to occur almost
simultaneously. It was concluded that the positive and
negative pressures at both sides of the brain, generated
due to the movement of the whole brain inside the skull,
traveled quickly toward the middle of the brain in the
form of stress waves [28], as shown in 4(a) and 4(c). Due
to the large bulk modulus of brain tissue compared to its
shear modulus, the pressure responses within the
cranium reached hydrostatic balance almost
instantaneously [21]. Therefore, the pressure responses at
different locations inside the brain reached their peak
values almost at the same time.
While the determination of ICP by numerical methods
appears relative straightforward, the detection, evaluation,
and validation of the shear stress are quite complicated.
Shear stress has been widely investigated in many
studies and several injury thresholds have been defined
based on that [21]. Fig. 5 shows how shear waves
propagated throughout the brain tissue. Due to the low
shear modulus of the brain tissue (compared with its high
bulk modulus), the shear waves propagated slowly, when
compared to the pressure wave propagation [28]. Similar
to the pressure behavior, at the instant of the impact,
shear stresses were also generated at the coup and
countercoup sites of the brain, and propagated from both
sides toward the middle of the brain. However, unlike the
attenuating pattern of the pressure wave, shear stresses
were notably amplified inside the brain. It was concluded,
therefore, that the determination of shear stresses inside
the brain needed a thorough validation of the head
models against the wave propagation.
Figure 5. Maximum shear stress responses of the NDSUFEHM for (a)
low-velocity impact; (b) High-velocity impact
Figure 6. (a) ICP and (b) shear stress distribution in the brain upon
impact at 10 m/s velocity
It has been postulated that the development of
pressure gradients inside the brain can give rise to shear
stresses deep inside the brain [29]. In other words, an
accurate determination of maximum shear stresses
(proportional to the difference between the first and third
principal stresses) requires a precise evaluation of
pressure waves. As the shear modulus of the brain (on
the order of kPa) is far smaller than its bulk modulus (on
the order of GPa), a slight deviation of principal stress
values (or pressures) inside the brain may result in a
greater deviation in the prediction of maximum shear
stresses. Another consideration in affecting brain
maximum shear stress could be the element size [28] as
stress concentration may occur adjacent to large elements.
In terms of the risk of injury, it is seen that the higher
speed impacts expose the brain to higher risks of
concussive injury. Zhang et al. [5] found 235 kPa to be
threshold for mild TBI. While the peak coup ICP was
175 kPa for the 10 m/s, it was increased to about 290 kPa
for the 13 m/s impact which put the brain at a serious
risk of concussive injuries. Maximum shear stress is used
as the criterion for DAI. Zhang et al. [5] found the
threshold for disuse injury to be shear stresses exceeding
7.8 kPa. For both the MSS was under 3 kPa in both
impacts so risks of DAI was assumed to very low.
Moreover, it was observed that there was no
correlation between the impact intensity and the ICP and
MSS peak values. This could be due to the difference in
shape, material, and functions of different parts of the
brain.
IV. CONCLUSION & FUTURE WORKS
NDSUFE head model was used to study the
mechanism of impact-induced TBI as it was impacted by
an impactor at two 10 m/s and 13 m/s velocities. The
maximum and minimum pressures were found on the
brain surface and were shown to vanish toward the center
of the brain. The ICP varied linearly from the coup to the
counter coup sites inside the brain very quickly such that
the whole brain tolerated the pressure simultaneously.
Shear stress, on the other hand, showed a very different
pattern compared to that of the ICP. While the pressure
vanished quickly after a few milliseconds, the shear
stress showed a phase lag and travelled inside the brain
much slower due to the brain viscous behavior.
Additionally, several milliseconds after the external
loads and pressures disappeared, the brain experienced
significant shear stress peaks at several locations.
0
0.4
0.8
1.2
1.6
2
0 4 8 12 16
Ma
x.
Sh
ea
r S
tres
s (
kP
a)
Time (ms)
0
0.5
1
1.5
2
2.5
3
0 4 8 12 16
Ma
x.
Sh
ea
r S
tres
s (
kP
a)
Time (ms)
(b)
(a)
(a) (b)
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© 2019 Int. J. Mech. Eng. Rob. Res 926
Therefore, a head model only validated against ICP
cannot be considered as sufficiently validated against
other mechanical parameters relevant to brain injury.
While our research addresses a very significant challenge,
the authors believe some future works can further boosts
this study. We plan to incorporate other FE head models
and compare our results with them to investigate the
accuracy of different FE head models. Furthermore, it
would be beneficial to include impacts from other
directions and it higher intensities to investigate the
effects of impact velocity and direction. Finally,
reconstruction of real impact events such as those
happening in football or hockey can expand the scope of
this study.
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Dr. Hesam S. Moghaddam is a Lecturer of
Mechanical Engineering at Northern Arizona
University in Flasgtaff AZ and is currently teaching Engineering Design courses. He
joined NAU in 2017 after teaching at Harvey
Mudd College as a visiting Assistant Professor for the 2016-2017 academic year.
At Harvey Mudd, he taught courses such as
Fluid Mechanics, Biomechanics, and Engineering Design. Prior to his time at
Harvey Mudd, Hesam worked as a Postdoctoral Research Fellow at the
department of surgery at UC San Francisco. There he contributed to the biomedical engineering research on aortic aneurysms and transcatheter
aortic valves. Hesam received his Ph.D. in Mechanical Engineering
from North Dakota State University (NDSU) in August 2015. His research was focused on computational modeling of traumatic brain
International Journal of Mechanical Engineering and Robotics Research Vol. 8, No. 6, November 2019
© 2019 Int. J. Mech. Eng. Rob. Res
International Journal of Mechanical Engineering and Robotics Research Vol. 8, No. 6, November 2019
© 2019 Int. J. Mech. Eng. Rob. Res 927
injury under dynamic loading specially blast loads. Hesam was awarded the Brain Injury Fellowship by North American Brain Injury
Society for his contributions in the field of traumatic brain injury.
Hesam has published more than 20 peer-reviewed articles in well-known journals and conferences.
Prof. Mariusz Ziejewski, is a Professor in
the College of Engineering at North Dakota State University where he is the director of
the Impact Biomechanics Laboratory and the
director of the Automotive Systems Laboratory. Dr. Ziejewski is also an Adjunct
Professor in the Department of Neuroscience
at the University of North Dakota School of Medicine. Dr. Ziejewski has performed
human body dynamics research for the
Armstrong Aerospace Medical Research
Laboratory, Human System Division which is part of the United States
Air Force. He has been a member of the National Highway Traffic
Safety Administration (NHTSA) Collaboration Group on Human Brain Modeling. He has been involved in Emergency Room (ER)
Biomechanical Brain Injury Evaluation, at Meritcare’s Trauma Center,
Fargo, ND. Dr. Ziejewski was also named the founding chair of the Blast Injury Institute of NABIS. Over the years he has received many
research grants, currently one of his grants is half a million-dollar
contract focusing on “Blast and the Consequences on Traumatic Brain Injury – Multiscale Mechanical Modeling of Brain.” A second grant of
a 0.6 million dollars, “Blast Pressure Gradients and Fragments on
Ballistic Helmets and the Head and Brain Injury-Simultaneous Multiscale Modeling with Experimental Validationʺ was accepted for
funding. Dr. Ziejewski has published three book chapters on brain and
neck injury and over eighty technical refereed articles.
Prof. Ghodrat Karami is a Professor in the
College of Engineering at North Dakota State University where he is also the graduate
coordinator for the mechanical engineering
program. Dr. Karami has performed many numerical analyses of traumatic brain injury
under dynamic loading such as impact and
blast. Dr. Karami has been awarded the “Researcher of the Year” award due to his
accomplishments in the field of brain injury.
He has published more than peer-reviwed journal papers in many prestigious engineering journals. His research activities include the
entire human body focusing on head/neck dynamics. Over the years he
has received many research grants, currently one of his grants is half a million-dollar contract focusing on “Blast and the Consequences on
Traumatic Brain Injury –
Multiscale Mechanical Modeling of Brain.” A
second grant of a 0.6 million dollars, “Blast Pressure Gradients and Fragments on Ballistic Helmets and the Head and Brain Injury-
Simultaneous Multiscale Modeling was accepted for funding.
Dr. Asghar Rezaei is currently a
postdoctoral research fellow in the
department of physiology and biomedical engineering at Mayo clinic. Dr. Rezaei has
carried out many experimental and numerical
analyses on traumatic brain injury from material characterization of brain tissue to
understanding the biomechanics of brain
injury under blast. His current research is on the bone fracture.
International Journal of Mechanical Engineering and Robotics Research Vol. 8, No. 6, November 2019
© 2019 Int. J. Mech. Eng. Rob. Res
International Journal of Mechanical Engineering and Robotics Research Vol. 8, No. 6, November 2019
© 2019 Int. J. Mech. Eng. Rob. Res 928